Sparse regularization for fiber ODF reconstruction: from the suboptimality of ℓ2 and ℓ1 priors to ℓ0.

Diffusion MRI is a well established imaging modality providing a powerful way to probe the structure of the white matter non-invasively. Despite its potential, the intrinsic long scan times of these sequences have hampered their use in clinical practice. For this reason, a large variety of methods have been recently proposed to shorten the acquisition times. Among them, spherical deconvolution approaches have gained a lot of interest for their ability to reliably recover the intra-voxel fiber configuration with a relatively small number of data samples. To overcome the intrinsic instabilities of deconvolution, these methods use regularization schemes generally based on the assumption that the fiber orientation distribution (FOD) to be recovered in each voxel is sparse. The well known Constrained Spherical Deconvolution (CSD) approach resorts to Tikhonov regularization, based on an ℓ(2)-norm prior, which promotes a weak version of sparsity. Also, in the last few years compressed sensing has been advocated to further accelerate the acquisitions and ℓ(1)-norm minimization is generally employed as a means to promote sparsity in the recovered FODs. In this paper, we provide evidence that the use of an ℓ(1)-norm prior to regularize this class of problems is somewhat inconsistent with the fact that the fiber compartments all sum up to unity. To overcome this ℓ(1) inconsistency while simultaneously exploiting sparsity more optimally than through an ℓ(2) prior, we reformulate the reconstruction problem as a constrained formulation between a data term and a sparsity prior consisting in an explicit bound on the ℓ(0)norm of the FOD, i.e. on the number of fibers. The method has been tested both on synthetic and real data. Experimental results show that the proposed ℓ(0) formulation significantly reduces modeling errors compared to the state-of-the-art ℓ(2) and ℓ(1) regularization approaches.

Home Childcarer Approval Scheme Application Form HCC1 (PDF 62.3KB)

Home Childcarer Approval Scheme Application Form HCC1

Early Years Home Childcare Approval Scheme FAQ (PDF 40.2KB)

Early Years Home Childcare Approval Scheme - frequently asked questions

Degree in Social Work Incentive Scheme 2006 (PDF 45 KB)

Student Bursaries Incentive Scheme

Craigavon & Banbridge Community HSS Trust - Primary Care Mental Health Services Triage Pilot Scheme (PDF 266 KB)

Craigavon & Banbridge Community HSS Trust's final report on Primary Care Mental Health Services Triage Pilot Scheme. Part of the Department's redesign of community nursing project.

HPSS Consultant and Distinction Awards Scheme (DMSAC)

HPSS Consultant and Distinction Awards Scheme (DMSAC)

New HPSS Clinical Excellence Awards Scheme (PDF 42 KB)

New HPSS Clinical Excellence Awards Scheme

Literature Review: Equality of Opportunity in Relation to the DHSSPS Draft Equality Scheme

This review of the literature on equality of opportunity issues was commissioned by the Department of Public Health, Social Sevices and Public Safety.

Performance-Related Awards: Health Boards Scheme

Performance-Related Awards: Health Boards Scheme This progress report to September 2003 on the performance-related awards scheme for senior health board management has been prepared by the Committee for Performance Awards for the Health Board Scheme, in line with the recommendation in Report No. 38 of the Review Body for Higher Remuneration in the Public Sector, to contribute to the Review Bodyâ?Ts consideration at its next general review (para 13.4). Click here to download PDF 93kb

Review of the Nursing Home Subvention Scheme

Review of the Nursing Home Subvention Scheme The government decided in 1997 to approve proposals from the Minister for Finance for a process of expenditure reviews as a key part of the financial management systems that are central to the Strategic Management Initiative and are intended to ensure greater predictability in resource planning. The aims of the expenditure review process are as follows: Click here to download PDF 873kb